Higher-Order Approximations for Verification of Stochastic Hybrid Systems

This work investigates the approximate verification of probabilistic specifications expressed as any non-nested PCTL formula over Markov processes on general state spaces. The contribution puts forward new algorithms, based on higher-order function approximation, for the efficient computation of approximate solutions with explicit bounds on the error. Approximation error related to higher-order approximations can be substantially lower than those for piece-wise constant (zeroth-order) approximations known in the literature and, unlike the latter, can display convergence in time to a finite value. Furthermore, higher-order approximation procedures, which depend on the partitioning of the state space, can lead to lower partition cardinality than the related piece-wise constant ones. The work is first presented for Markov processes over Euclidean spaces and thereafter extended to hybrid spaces characterizing models known as Stochastic Hybrid Systems.